Distance Between Cities
How far apart two cities are, in a straight line over the curve of the Earth.
How it works
The distance is the great-circle distance — the shortest path across the surface of a sphere — worked out with the haversine formula from each city's latitude and longitude. It treats the Earth as a sphere of mean radius 6,371 km, which is accurate to about 0.5% against the true ellipsoid: a few kilometres on an intercontinental route.
The bearing is the initial heading. On a long great-circle route the heading changes continuously, which is why flight paths look curved on a flat map and why a plane to Tokyo may set off towards the pole.
Travel times are distance divided by a representative speed. They ignore roads, stops, take-off, landing and everything else that makes a real journey longer.
Examples
London to New York. About 5,570 kilometres as a great circle. A road or a shipping route would be far longer; this is the shortest path across the surface, which is what a flight approximates.
Why the plane goes north. The initial bearing from London to Tokyo is close to due north-east, and the route passes near the Arctic. On a flat map that looks like a detour; on a globe it is the direct line.
Estimating a flight time. Divide by a typical cruising speed for a rough figure, then add time for take-off, landing and routing — the estimate is a lower bound rather than a schedule.
Practical notes
The figure is a great-circle distance computed with the haversine formula, treating the Earth as a sphere of mean radius 6,371 km. That approximation is good to about half a percent against the true ellipsoid, which on an intercontinental route means a few kilometres.
The bearing given is the initial heading only. Along a great circle the heading changes continuously, so a constant-bearing course is a different and longer path. This is why flight paths look curved on a flat projection and why a plane to Tokyo can set off towards the pole.
Distances are between city reference points, not between airports or city edges, and travel times ignore roads, terrain, air traffic routing and every part of a journey that is not cruising.
Frequently asked questions
Why does this differ from the driving distance?
Because roads do not run in straight lines. This is the shortest path over the globe; a road route is always longer, often much longer where mountains or water intervene.
What is the initial bearing?
The compass heading you would set off on. It changes as you travel along a great circle, so it is only the starting direction, not a constant one.
How accurate is the distance?
Within roughly half a percent. The Earth is slightly flattened at the poles and this uses a spherical approximation.
Why is this shorter than the driving distance?
Because roads do not run in straight lines. This is the shortest path over the surface of the globe; any road route is longer, often substantially where mountains or water intervene.
What is a great circle?
The shortest path between two points on a sphere — the line a taut string would follow over a globe. It looks curved on a flat map only because the map is a distortion.
Why does the bearing change along the route?
Because a great circle crosses each meridian at a different angle. The figure given is the initial heading; holding it constant would take you somewhere else.
Are flight times reliable?
They are rough estimates from distance and a representative cruising speed. Real schedules add taxiing, climb, descent, routing and wind.
Can I compare more than two cities?
One pair at a time. For a multi-stop route, add the legs together, remembering that the sum of great circles is not itself a great circle.
Does it give the bearing back?
The return bearing is not simply the reverse, because a great circle crosses each meridian at a different angle.
How long would it take to drive?
These are great-circle distances over the surface, so most pairs are not drivable at all. Where they are, a road route is always longer than the figure shown.
Is the shortest route always the fastest?
Not for aircraft. Winds, airspace restrictions and diversion requirements all shift real routes away from the great circle, sometimes substantially.